Universal homogeneous causal sets

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.Comment: 14 page

Approximating Tverberg Points in Linear Time for Any Fixed Dimension

Let P be a d-dimensional n-point set. A Tverberg-partition of P is a partition of P into r sets P_1, ..., P_r such that the convex hulls conv(P_1), ..., conv(P_r) have non-empty intersection. A point in the intersection of the conv(P_i)'s is called a Tverberg point of depth r for P. A classic result by Tverberg implies that there always exists a Tverberg partition of size n/(d+1), but it is not known how to find such a partition in polynomial time. Therefore, approximate solutions are of interest. We describe a deterministic algorithm that finds a Tverberg partition of size n/4(d+1)^3 in time d^{O(log d)} n. This means that for every fixed dimension we can compute an approximate Tverberg point (and hence also an approximate centerpoint) in linear time. Our algorithm is obtained by combining a novel lifting approach with a recent result by Miller and Sheehy (2010).Comment: 14 pages, 2 figures. A preliminary version appeared in SoCG 2012. This version removes an incorrect example at the end of Section 3.

Biocontrol of potato wilt by selective rhizospheric and endophytic bacteria associated with potato plant

Ralstonia solanacearum is the causative agent of wilt disease in plants, which constitutes a severe problem to agricultural crops, particularly for potato production in Madagascar. The present study focuses on the isolation, in vitro and in vivo assays of potential rhizospheric and endophytic bacteria associated with healthy potato plant, capable to inhibit the growth of Ralstonia solanacearum for controlling potato bacterial wilt. A total of 77 bacteria strains were isolated from six soil rhizospheric samples and six vegetal material samples of healthy potatoes in the district of Antsirabe II. Forty of them were telluric actinomycetes, 25 were endophytic actinomycetes and 12 were fluorescent Pseudomonas spp. An additional 30 phytopathogenic isolates were obtained from six rhizopsheric soil samples of diseased potatoes. Morphological, cultural, biochemical characterization and molecular identification with the Ralstonia solanacearum specific primers 759/760 revealed that 24 of the pathogenic isolates belong to the Ralstonia solanacearum species, biovar two; the causal agent of potato bacterial wilt. Isolates from healthy plants were, then, examined in vitro and in vivo for their antagonistic activity against Ralstonia solanacearum strain for their potential to improve potato plant growth. In vitro antagonism of actinomycete and Pseudomonas isolates against Ralstonia solanacearum development was performed using agar diffusion technique, while in vivo tests were conducted under greenhouse conditions. Ten antagonistic strains including two Pseudomonas, four telluric actinomycetes, and four endophytic actinomycetes inhibited the tested Ralstonia strain. Four strains, E7, E13 (endophytic actinomycete from root potatoes), S25 (telluric actinomycetes) and P7 (fluorescent Pseudomonas), showed high antagonistic activity against the pathogen with zones of inhibition from 23 to 40 mm. Of the fours strains tested in greenhouse, E7 significantly reduced (p &lt; 0.05) the percentage of Ralstonia solanacearum that infected plants by 72.04%. The isolates E13 and S25 have also been demonstrated to improve plant growth by increase of plant height to 44.63% and 44.84%, fresh weight to 68.75% and 75.85% and dry weight to 86.17% and 115.42%, respectively compared with non-treated control. Morphological and cultural characterization of these three active isolates showed that they belong to the genus Streptomyces. The antagonism of these isolates against Ralstonia solanacearum according to in vitro and in vivo tests results, along with their high efficiency as regards the improvement of plant development, suggests that these three actinomycete strains E7, E13 and S25 could be useful for biocontrol of potato bacterial wilt.Key words: Potato, Ralstonia, Actinomycetes, Pseudomonas, Biocontrol

Stability of Bose Einstein condensates of hot magnons in YIG

We investigate the stability of the recently discovered room temperature Bose-Einstein condensate (BEC) of magnons in Ytrrium Iron Garnet (YIG) films. We show that magnon-magnon interactions depend strongly on the external field orientation, and that the BEC in current experiments is actually metastable - it only survives because of finite size effects, and because the BEC density is very low. On the other hand a strong field applied perpendicular to the sample plane leads to a repulsive magnon-magnon interaction; we predict that a high-density magnon BEC can then be formed in this perpendicular field geometry.Comment: Submitted to Physical Review Letter

Observation of thickness dependence of magnetic surface anisotropy in ultrathin amorphous films.

Copyright © 1990 The American Physical SocietyFerromagnetic resonance (FMR) and SQUID magnetometry measurements have been made on multilayers of amorphous Fe70B30/Ag. The dependence of the magnetic surface anisotropy constant Ks on the magnetic layer thickness 2L has been determined in the range 1.6 Å16.5 Å, but decreases monotonically towards zero as 2L decreases from 16.5 Å towards zero. The FMR results can be well described by a theory developed for ultrathin amorphous ferromagnetic layers

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set

Analogues of the central point theorem for families with dd-intersection property in Rd\mathbb R^d

In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families

Towards Autopoietic Computing

A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems increasingly difficult. Biological systems are thought to possess robust, scalable processing paradigms that can automatically manage complex, dynamic problem spaces, possessing several properties that may be useful in computer systems. The biological properties of self-organisation, self-replication, self-management, and scalability are addressed in an interesting way by autopoiesis, a descriptive theory of the cell founded on the concept of a system's circular organisation to define its boundary with its environment. In this paper, therefore, we review the main concepts of autopoiesis and then discuss how they could be related to fundamental concepts and theories of computation. The paper is conceptual in nature and the emphasis is on the review of other people's work in this area as part of a longer-term strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure